Cremona's table of elliptic curves

2850 = 2 · 3 · 5² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 19-	Signs for the Atkin-Lehner involutions
Class	2850l	Isogeny class
Conductor	2850	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	133229306250000 = 24 · 310 · 58 · 192	Discriminant
Eigenvalues	2+ 3- 5+ -4  0  6 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-769501,259748648]	[a1,a2,a3,a4,a6]
Generators	[412:3356:1]	Generators of the group modulo torsion
j	3225005357698077121/8526675600	j-invariant
L	2.7215475947486	L(r)(E,1)/r!
Ω	0.50670663492721	Real period
R	0.53710518220067	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	22800bv2 91200m2 8550bh2 570i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2850l2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-	+	-4	0	6	-2	-	-8	2	-8	-10	6	8	0	2	-12	-2	12	-8	-2	-16	4	6	10

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Quadratic twists for elliptic curve 2850l2

-4	8	-3	5	-19
22800bv2	91200m2	8550bh2	570i2	54150ca2

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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